Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “finite difference”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,261 records · Page 70
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Spatially resolved x-ray detection with photonic crystal scintillators

We study the self-collimation phenomenon in photonic crystals (PhC) of wide bandgap materials for ultra-fast and high spatial resolution x-ray detection. We work on various heavy inorganic scintillators: BaF 2 , GaN, ZnO, CsI:Tl, NaI:Tl, LYSO, WO 4 compounds, and plastic scintillators. Conventional scintillator detectors do not rely on a direct detection mechanism; hence, they require intricate design and fabrication processes. We offer a PhC design to observe self-collimation phenomena and overcome the ongoing spatial resolution challenges with these types of materials. We investigate the photonic band diagrams and iso-frequency contours. Fourier transforms based on finite-difference time-domain and frequency domain simulations are done for verifying and analyzing the self-collimation with the selected material. Light extraction efficiency at the PhC–air interface, depending on the truncation distance from the excitation point, is measured. Beam divergence values are calculated at 1 mm propagation distance. The vertical field profiles are obtained to observe the confinement. For the spatial resolution analysis, cross-sectional beam profiles have been examined. Furthermore, Gaussian envelopes are fitted to beam profiles for a consistent data analysis, and full-width-at-half-maximum values are considered. As a result, we theoretically prove and demonstrate the spatially resolved x-ray detection at the sub-micrometer level for a wide range of scintillator materials.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Few-cycle optical field breakdown and damage of gallium oxide and gallium nitride

Both gallium oxide and gallium nitride have great potential for use as high power transparent conducting oxide materials for a wide range of optoelectronic applications. It is, therefore, important to determine the dynamic optical field breakdown for these materials. Here, we report laser damage thresholds for Ga 2 O 3 and GaN using 9 fs few-cycle pulses with a center wavelength near 760 nm. We determine laser-induced damage thresholds (LIDTs) for both single pulse and multi-pulse exposures, with multi-pulse LIDT showing significant reduction compared to single pulse LIDT (in some cases, >50%), possibly due to laser-induced defects. We show that Ga 2 O 3 and GaN have an ultrafast optical field breakdown of 23 and 18 GV/m when nearly polarized along their [010] and [111] planes, respectively, extending their suitability for high power applications to the ultrashort pulse regime. To accurately characterize the excited carrier density criteria in which apparent laser damage occurs, carrier excitation dynamics for the entire laser pulse interaction were simulated using a modified Keldysh ionization model. For the measured single-shot threshold fluences, the plasma critical density was surpassed by 2 orders of magnitude and 2D finite-difference time-domain simulations were employed to understand the pulse interaction near the surface.

Tripepi, Michael↗
DOE OSTI2023

Quantum efficiency enhancement in simulated nanostructured negative electron affinity GaAs photocathodes

We report nanostructured negative electron affinity GaAs photocathodes for a polarized electron source are studied using finite difference time domain optical simulation. The structures studied are nanosquare columns, truncated nanocones, and truncated nanopyramids. Mie-type resonances in the 700–800 nm waveband, suitable for generation of polarized electrons, are identified. At resonance wavelengths, the nanostructures can absorb up to 99% of the incident light. For nanosquare columns and truncated nanocones, the maximum quantum efficiency (QE) at 780 nm obtained from simulation is 27%, whereas for simulated nanopyramids, the QE is ~21%. The high photocathode quantum efficiency is due to the shift of Mie resonance toward the longer wavelength, leading to increased light absorption. The field profile distribution shows the excitation of dipole and quadrupole modes within the nanostructures at resonant frequencies. This leads to enhanced photoabsorption and photoelectron generation closer to emission surfaces than for a flat photocathode. The enhanced photoabsorption and reduced electron transport distance for the nanostructured photocathode enhance its QE compared to that for the flat surface wafer.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Real-space solution to the electronic structure problem for nearly a million electrons

We report a Kohn–Sham density functional theory calculation of a system with more than 200 000 atoms and 800 000 electrons using a real-space high-order finite-difference method to investigate the electronic structure of large spherical silicon nanoclusters. Our system of choice was a 20 nm large spherical nanocluster with 202 617 silicon atoms and 13 836 hydrogen atoms used to passivate the dangling surface bonds. To speed up the convergence of the eigenspace, we utilized Chebyshev-filtered subspace iteration, and for sparse matrix–vector multiplications, we used blockwise Hilbert space-filling curves, implemented in the PARSEC code. For this calculation, we also replaced our orthonormalization + Rayleigh–Ritz step with a generalized eigenvalue problem step. We utilized all of the 8192 nodes (458 752 processors) on the Frontera machine at the Texas Advanced Computing Center. We achieved two Chebyshev-filtered subspace iterations, yielding a good approximation of the electronic density of states. Our work pushes the limits on the capabilities of the current electronic structure solvers to nearly 106 electrons and demonstrates the potential of the real-space approach to efficiently parallelize large calculations on modern high-performance computing platforms.

Chemistry↗
DOE OSTI2023

Ballooning theory for micro-tearing mode in tokamak

This paper aims to investigate the impact of magnetic drift on the linear micro-tearing mode by using a kinetic approach to derive a reduced two-field eigen system in real space. Here, since the magnetic drift in real space has derivatives, it is more efficient to solve the mode equations in a Fourier-ballooning representation using the two-dimensional (2D) ballooning transform. The lowest-order eigen system in the Fourier-ballooning representation consists of two integral equations, which are numerically solved using the finite difference method for both eigenvalues and wave functions. The main results will be presented through graphical eigenvalue scans for each parameter. Furthermore, we present a graphical comparison between the predictions of the ballooning theory and GENE gyrokinetic code simulation in the pedestal region.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Topanga: A kinetic ion plasma code for large-scale ionospheric simulations on magnetohydrodynamic timescales

Topanga is a kinetic ion code developed for simulating large-scale plasma phenomena in the Earth's ionosphere on magnetohydrodynamic timescales. It is a domain-decomposed parallel code that runs on high-performance computing platforms. Features of Topanga include spherical geometry for simplified boundary conditions and computational efficiency; a hybrid plasma model with inertia-less fluid electrons, kinetic ions, and an electric field specified via an Ohm's law; a Maxwell-FDTD (finite difference time domain) plasma model which retains the displacement current in Maxwell's equations and models electron currents in the ionosphere with a tensor conductivity; sponge-layer boundary conditions for absorption of electromagnetic and plasma waves incident on the domain boundaries; and a novel mixed-implicit algorithm for evolving the EM fields inside the Maxwell-FDTD region that is stable over many orders of magnitude in the electron–ion collision frequency. We verify the numerical methods used in Topanga on a pair of test problems. The first test involves modeling a three-dimensional collisionless shock using the hybrid set of equations. The second test involves modeling a spherical TEM mode in vacuum using the Maxwell-FDTD set of equations. Finally, we demonstrate how using the combined set of hybrid and Maxwell-FDTD equations to model the Starfish Prime high-altitude nuclear test recovers a “missing” EM signal on the ground that is not present when using only the hybrid set of equations. The magnitude of this signal in the simulation containing the Maxwell-FDTD region agrees well with the E3a portion of the magnetohydrodynamic electromagnetic pulse from Starfish Prime.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Characterization of electromigration-induced short-range stress development in Al(0.25 at. % Cu) conductor line

Scanning x-ray microbeam topography and fluorescence experiments were conducted in situ to study the electromigration behavior of a 0.5 μm thick, 10 μm wide, and 200 μm long Al(0.25 at. % Cu) conductor line with 1.5 μm-thick SiO2 passivation on a single crystal Si substrate. The strain sensitivity of x-ray topography measurement allowed detailed examination of the electromigration-induced stress distribution and evolution in the conductor line in response to the depletion of Cu solute early in the electromigration process. Upon electromigration at 0.4 MA/cm2 and 303 °C, a short-range stress gradient was quickly induced by Al migration in the Cu-depleted cathode region to counteract further Al flow. The stress gradient was fully developed during the 5.3 h incubation time, extending over the critical Blech length of about 66 μm from the cathode end. Plastic deformation then occurred at the downstream end of the Cu-depleted region. The preferential electromigration of Cu did not cause detectable stress change outside the Cu-depleted region, except for the significant stress development from the Al2Cu precipitation at the anode end which appeared to initiate the fracture in the passivation. Preliminary finite difference modeling was undertaken to simulate the experimental observations, from which important parameters dictating electromigration in Al(Cu) line were extracted: an apparent effective valence of −5.6 and −1.9 for Cu and Al in Al(Cu), respectively, and a critical Cu concentration of 0.16 at. % above which Al grain boundary diffusion is effectively blocked.

Physics↗
DOE OSTI2024

Voltage-induced modulation of interfacial ionic liquids measured using surface plasmon resonant grating nanostructures

We have used surface plasmon resonant metal gratings to induce and probe the dielectric response (i.e., electro-optic modulation) of ionic liquids (ILs) at electrode interfaces. Here, the cross-plane electric field at the electrode surface modulates the refractive index of the IL due to the Pockels effect. This is observed as a shift in the resonant angle of the grating (i.e., Δϕ), which can be related to the change in the local index of refraction of the electrolyte (i.e., Δnlocal). The reflection modulation of the IL is compared against a polar (D2O) and a non-polar solvent (benzene) to confirm the electro-optic origin of resonance shift. The electrostatic accumulation of ions from the IL induces local index changes to the gratings over the extent of electrical double layer (EDL) thickness. Finite difference time domain simulations are used to relate the observed shifts in the plasmon resonance and change in reflection to the change in the local index of refraction of the electrolyte and the thickness of the EDL. Simultaneously using the wavelength and intensity shift of the resonance enables us to determine both the effective thickness and Δn of the double layer. We believe that this technique can be used more broadly, allowing the dynamics associated with the potential-induced ordering and rearrangement of ionic species in electrode–solution interfaces.

Chemistry↗
DOE OSTI2024

MolSym : A Python package for handling symmetry in molecular quantum chemistry

A consideration of the point group symmetry of molecules is often advantageous from a computational efficiency standpoint and sometimes necessary for the correct treatment of chemical physics problems. Many modern electronic structure software packages include a treatment of symmetry, but these are sometimes incomplete or unusable outside of that program’s environment. Therefore, we have developed the MolSym package for handling molecular symmetry and its associated functionalities to provide a platform for including symmetry in the implementation and development of other methods. Features include point group detection, molecule symmetrization, arbitrary generation of symmetry element sets and character tables, and symmetry adapted linear combinations of real spherical harmonic basis functions, Cartesian displacement coordinates, and internal coordinates. We present some of the advantages of using molecular symmetry as achieved by MolSym, particularly with respect to Hartree–Fock theory, and the reduction of finite difference displacements in gradient/Hessian computations. Furthermore, this package is designed to be easily integrated into other software development efforts and may be extended to further symmetry applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

An octahedral Mach B-dot probe for 3D flows and magnetic fields in the edge of reversed field pinches

Measurements and simulations show that plasma relaxation processes in the reversed field pinch drive and redistribute both magnetic flux and momentum. To examine this relaxation process, a new 3D Mach B-dot probe has been constructed. This probe collects ion saturation currents through six molybdenum electrodes arranged on the flattened vertices of an octahedron made of boron nitride (BN). The ion saturation current flows through configurable voltage dividers for measurement and returns through one of six selectable return electrodes equally spaced along the 12 cm BN probe arm. In addition, the probe arm houses three B-dot magnetic pickup coils in the BN stalk immediately below to the octahedron, to measure the local magnetic field. Inserted in the Madison Symmetric Torus (MST) during deuterium discharges with 220 kA plasma current, density of 0.8 × 10 13 cm –3 , the probe collects ion saturation currents with sawtooth-like peaks correlated with relaxation events. This compact octahedral design fitting six Mach electrode surfaces within a 1 cm3 cube will enable future multi-point, multi-field probes compatible with the 1.5 in. ports of MST. Such probes will allow for flow circulation, current, and canonical vorticity to be calculated in the center of the finite difference stencil formed by the measurement locations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Harnessing complexity: Nonlinear optical phenomena in L-shapes, nanocrescents, and split-ring resonators

Here, we conduct systematic studies of the optical characteristics of plasmonic nanoparticles that exhibit C 2v symmetry. In particular, we analyze three distinct geometric configurations: an L-type shape, a crescent, and a split-ring resonator shaped like the Greek letter π. Optical properties are examined using the finite-difference time-domain method. It is demonstrated that all three shapes exhibit two prominent plasmon modes associated with the two axes of symmetry. This is in addition to a wide range of resonances observed at high frequencies corresponding to quadrupole modes and peaks due to sharp corners. Next, to facilitate nonlinear analysis, we employ a semiclassical hydrodynamic model, where the electron pressure term is explicitly accounted for. This model goes beyond the standard Drude description and enables capturing nonlocal and nonlinear effects. Employing this model enables us to rigorously examine the second-order angular resolved nonlinear optical response of these nanoparticles in each of the three configurations. Two pumping regimes are considered, namely, continuous wave (CW) and pulsed excitations. For CW pumping, we explore the properties of the second harmonic generation (SHG). Polarization and angle-resolved SHG spectra are obtained, revealing strong dependence on the nanoparticle geometry and incident wave polarization. The C 2v symmetry is shown to play a key role in determining the polarization states and selection rules of the SHG signal. For pulsed excitations, we discuss the phenomenon of broadband terahertz (THz) generation induced by the difference-frequency generation . It is shown that the THz emission spectra exhibit unique features attributed to the plasmonic resonances and symmetry of the nanoparticles. The polarization of the generated THz waves is also examined, revealing interesting patterns tied to the nanoparticle geometry. To gain deeper insight, we propose an analytical theory that agrees very well with the numerical experiments. The theory shows that the physical origin of the THz radiation is the mixing of various frequency components of the fundamental pulse by the second-order nonlinear susceptibility. An expression for the far-field THz intensity is derived in terms of the incident pulse parameters and the nonlinear response tensor of the nanoparticle. The results presented in this work offer new insights into the linear and nonlinear optical properties of nanoparticles with C 2v symmetry. The demonstrated strong SHG response and efficient broadband THz generation hold great promise for applications in nonlinear spectroscopy, nanophotonics, and optoelectronics. The proposed theoretical framework also provides a valuable tool for understanding and predicting the nonlinear behavior of other related nanostructures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Efficient real space formalism for hybrid density functionals

We present an efficient real space formalism for hybrid exchange-correlation functionals in generalized Kohn–Sham density functional theory (DFT). In particular, we develop an efficient representation for any function of the real space finite-difference Laplacian matrix by leveraging its Kronecker product structure, thereby enabling the time to solution of associated linear systems to be highly competitive with the fast Fourier transform scheme while not imposing any restrictions on the boundary conditions. We implement this formalism for both the unscreened and range-separated variants of hybrid functionals. We verify its accuracy and efficiency through comparisons with established planewave codes for isolated as well as bulk systems. In particular, we demonstrate up to an order-of-magnitude speedup in time to solution for the real space method. We also apply the framework to study the structure of liquid water using ab initio molecular dynamics, where we find good agreement with the literature. Overall, the current formalism provides an avenue for efficient real-space DFT calculations with hybrid density functionals.

Chemistry↗
DOE OSTI2025

Efficient wind farm layout optimization with the FLOWERS AEP model and analytic gradients

Wind farm layout optimization (WFLO) studies often aim to maximize the annual energy production (AEP) of a wind farm by choosing an arrangement of turbines that minimizes wake interactions. One way to reduce the cost of WFLO studies is by using more computationally efficient AEP models. The cost of standard AEP modeling approaches, based on the numerical integration of low-fidelity engineering wake models, scales poorly with the number of simulated discrete wind conditions. A second way to reduce cost when using a gradient-based algorithm is to supply exact gradient information instead of finite-difference estimates. However, analytical functions for the derivatives of AEP with respect to turbine positions are not always available in the conventional modeling approach. FLOWERS is a computationally inexpensive, analytical model for wind farm AEP that is specifically developed for WFLO applications. In this paper, we analyze the performance of the FLOWERS AEP model with analytic gradients in a layout optimization study compared with a reference optimization framework across three wind farm case studies. We find that the FLOWERS-based approach reduces computation time by a factor of 50–4000 and improves optimal AEP by about 0.3% with less than half of the variability in AEP across instances with randomized initial conditions. We also find the optimal layouts to be insensitive to model parameter tuning, making FLOWERS-based layout optimization a streamlined, user-friendly approach.

17 WIND ENERGY↗
DOE OSTI2025

Ab-initio simulation of spin-vibronic spectra of methoxy radical

Despite the fact that experimental and theoretical work on the spectrum of methoxy has stretched from the microwave to the ultraviolet and proceeded for nearly 50 years, parts of the spectrum have remained a challenge to simulate theoretically and make reliable line-by-line assignments. The spectral complexity arises because the radical has a non-zero electron spin and significant vibronic coupling between the two elec- tronic components of the ground state due to the presence of a conical intersection. This work describes a completely ab initio effort to understand and assign the spin- vibronic levels of the X 2E state from 0 to above 3000 cm−1, a region that includes the fundamental transitions of the C-H symmetric and asymmetric stretches that have not previously been identified uniquely. A potential energy surface for methoxy was calculated at the EOM-CCSDT/ANO1 level of theory. Subsequently this potential energy surface was fit to a quartic power series expansion of all nine vibrational nor- mal coordinates (as determined at the minimum of the conical intersection) by the use of a machine-learning-based algorithm. After the addition of spin-orbit coupling, the spin-vibronic problem was solved using both the Krylov-Schur and Lanczos algorithms with the SOCJT3 software to converge eigenvalues up to 3500 cm−1 and their eigen- vectors. The latter were used, in conjunction with the calculated dipole moment and its derivatives (calculated using finite differences at EOM-CCSDT/ANO1 level), to determine spectral intensities for the spin-vibronic spectra. The calculated transition frequencies and intensities were used to simulate and assign the observed transitions of the spin-vibronic spectra of the radical. The credibility of the assignments and their significance is discussed in detail.

Sharma, Ketan [University of Florida, Gainesville,↗
DOE OSTI2025

PIAFS: A 2D nonlinear hydrodynamics code to model gaseous optics

The survivability of final optics is expected to be a major challenge for all future inertial fusion energy concepts. Due to their higher damage threshold, gaseous optics have been identified as a promising solution to this problem. Gaseous optics can be created through the photoabsorption of spatially modulated UV light, which induces various chemical processes that heat the gas. This heating leads to a pressure perturbation, which in turn launches a density perturbation that can imprint a refractive index modulation such as a grating. In this article, we introduce a parallel C/C++ code to simulate gaseous optics. PIAFS2D is a high-order conservative finite-difference code to solve the compressible Navier–Stokes equations along with the photochemical heating sources on Cartesian grids. The simulations are validated by the linear theory derived in a previous paper [Michel et al., Phys. Rev. Appl. 22, 024014 (2024)]. For larger perturbations, the behavior of the system—particularly the evolution of the generated acoustic wave—demonstrates strong nonlinearity. PIAFS2D allows the study of nonlinear behaviors and can be used for the design of high-efficiency gaseous optics elements in realistic experimental conditions.

Oudin, A. [Lawrence Livermore National Laboratory ↗
DOE OSTI2021

Multilevel-in-Space-and-Energy CMFD in VERA

For full-core modeling in the Virtual Environment for Reactor Analysis (VERA), the three-dimensional multigroup eigenvalue neutron transport problem is solved by MPACT. To improve the efficiency of MPACT, advancements have been made in the transport accelerator. Multilevel-in-energy and multilevel-in-space coarse mesh finite difference (CMFD) solvers were developed to improve the efficiency of the CMFD accelerator. In this paper a new multilevel-in-space-and-energy CMFD solver is developed with coarsening in both space and energy on every level. Several different strategies are investigated for coarsening groups in energy. Modified V-cycle and multiple-cycle algorithms are evaluated for solving the multilevel equations. The performance of these solvers is compared for typical full-core reactor physics problems.

42 ENGINEERING↗
DOE OSTI2022

Introduction of the Adding and Doubling Method for Solving Bateman Equations for Nuclear Fuel Depletion

This paper introduces and evaluates the Adding and Doubling Method (ADM) for solving the Bateman equations for depletion systems with varying numbers of nuclides and compares it to the Chebyshev Rational Approximation Method (CRAM), both implemented in the reactor physics analysis application Griffin. ADM, when applied to the Crank-Nicolson Finite Difference method, can produce results comparable in accuracy and precision to CRAM with comparable run times for systems with 35 or 297 nuclides. For systems with more than 300 nuclides, the matrix-matrix operations required by ADM are significantly more costly than the matrix-vector operations required by CRAM, making CRAM the more efficient method for systems with large numbers of nuclides. ADM is an accurate method that maintains other advantages over CRAM in that it does not depend on pre-generated coefficients or require complex number operations. ADM also manages to outperform CRAM by a factor of more than 250 in terms of run time for depletion systems that require multiple Bateman solves while the depletion matrix and time step size remain constant over all depletion intervals.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Sequential Learning of Active Subspaces

This study shows that in recent years, active subspace methods (ASMs) have become a popular means of performing subspace sensitivity analysis on black-box functions. Naively applied, however, ASMs require gradient evaluations of the target function. In the event of noisy, expensive, or stochastic simulators, evaluating gradients via finite differencing may be infeasible. In such cases, often a surrogate model is employed, on which finite differencing is performed. When the surrogate model is a Gaussian process (GP), we show that the ASM estimator is available in closed form, rendering the finite-difference approximation unnecessary. We use our closed-form solution to develop acquisition functions focused on sequential learning tailored to sensitivity analysis on top of ASMs. We also show that the traditional ASM estimator may be viewed as a method of moments estimator for a certain class of GPs. We demonstrate how uncertainty on GP hyperparameters may be propagated to uncertainty on the sensitivity analysis, allowing model-based confidence intervals on the active subspace. Our methodological developments are illustrated on several examples.

97 MATHEMATICS AND COMPUTING↗